Administrators at six D.C. public schools violated rules on standardized tests in the 2013-2014 school year by steering students to correct answers, erasing stray marks on answer sheets, or providing unauthorized accommodations for test takers, according to an annual test-security review.

The investigation — done by the outside consulting firm Alvarez & Marsal — found “minor” or “moderate” violations at 11 schools, including procedural errors such as missing test-security documentation or improperly signing out or returning test materials.

Nearly 33,000 students at 195 traditional and charter schools took the District of Columbia Comprehensive Assessment System tests in reading and math in spring 2014, and city officials said that confirmed violations represented just 0.5 percent of all testing groups and that most of the violations amounted to procedural or documentation errors.

Test scores — which are important factors in school ratings and decisions about teacher employment and salaries — have been under scrutiny in the District since shortly after former schools chancellor Michelle Rhee began leading the public school system in 2007 and implemented sweeping reforms. One investigation by USA Today found that more than 100 schools between 2008 and 2010 had high rates of wrong-to-right erasures, which can be an indication of possible cheating.

Other analyses have not found widespread evidence of cheating at D.C. schools, but D.C. has placed emphasis on test security in recent years.

“The data we receive from annual testing provides critical insights to student performance in schools across the District,” said State Superintendent Hanseul Kang in a statement. “It is imperative that our testing protocols and procedures reflect the highest levels of security so that our data is accurate.”

The report released by the Office of the State Superintendent of Education found critical violations in the administration of tests at two charter schools and four traditional public schools in 2014.

At Center City Public Charter School on Capitol Hill, students told investigators that a test administrator coached students to revisit certain answers, saying such things as ‘good job’ or ‘fix that problem.’ They also said they had seen one of the stories in the reading section before test day.

The school also was missing its “test security file,” which is required to contain documentation showing that proctors completed test-security training, followed test administration guidelines and signed test-security and nondisclosure agreements.

Russ E. Williams Jr., president and chief executive of Center City, which has six campuses in the District, called the violations an “isolated incident,” and said that the teacher who administered the test and the leadership team no longer work for Center City.

“We have taken several actions since the incident to prevent a situation like this from occurring again, including reinforcing the importance of test security and implementing additional training and reviews for staff to ensure tighter controls moving forward,” Williams wrote in an e-mail.

The class in question was originally flagged for investigation because students had high rates of erasures, changing answers from wrong to right. Students in the group had an average of 23 wrong-to-right erasures in math and 25 in reading; the citywide average was one in each subject.

The administrator said she taught students to use a process-of-elimination strategy that left stray marks that were then erased. The report said such a practice “likely inflated” the erasures but noted that such a strategy violates test-taking directions; students are told to fill in only the circle that goes with their chosen answer.

Paul Public Charter School’s middle school campus was the only school given a critical violation school-wide. The middle school in Ward 4 had been classified as a top-tier school by the D.C. Public Charter school board for three years before its scores were invalidated for 2014.

Administrators told investigators that at the end of each testing day, they, along with proctors, reviewed answer booklets and erased stray marks and filled in partially filled answer bubbles.

Jami Dunham, the school’s chief executive, said administrators readily admitted what they did because they did not know that it was improper; they said they did not change student answers.

The city report did not find that any answers were changed, and an internal school investigation corroborated that finding, Dunham said. Test-security policies and guidelines forbid altering test items in any way.

Dunham said the school disagreed with the city’s decision to invalidate its scores and unsuccessfully appealed the ruling.

D.C. Public Schools had four schools cited for critical violations: Cardozo Education Campus, Columbia Heights Education Campus, Dunbar High and Hendley Elementary. The schools were cited for giving unauthorized testing accommodations for some special education students, such as reading questions aloud to students who did not require that accommodation.

Michelle Lerner, a spokeswoman for D.C. Public Schools, said the report found no evidence of widespread problems with the school system’s test administration. “Our teachers and staff administered the test according to protocol with a few isolated cases of human error,” she said.

The investigation did not include the most recent administration of tests last spring using the new PARCC exams, a computer-based test aligned to Common Core state standards. A separate investigation of test security in 2015 will begin later this year, OSSE officials said.